1. Field of the Invention
The present invention relates to a hologram observation method for a radio wave hologram and an acoustic wave hologram, an estimation method for estimating a stereoscopic directivity of an antenna based on the radio wave hologram observation and a wave distribution observation method based on the radio wave hologram observation. The present invention particularly relates to an observation method which can precisely evaluate a reflected wave particularly in a propagation measurement of the radio wave and the acoustic wave and can precisely obtain a three-dimensional wave source distribution, to a method which can estimate a stereoscopic directivity of the antenna under its actual working state in set-up circumstances, to a method for visualizing current distribution and electromagnetic wave radiation on a high frequency circuit board or the like, and to a display method suitable for indicating a vector flow like the current distribution.
2. Description of the Prior Art
Visualization of an electromagnetic wave source by means of a radio wave hologram technology employing interference properties of an electromagnetic wave has been put to practical use, which is used for measuring a high frequency current distribution in a measurement objective and for reducing an unnecessary electromagnetic wave radiation. A hologram can be obtained not only by using the radio wave but also by using a acoustic wave, so that the hologram is made useful for specifying a noise source by visualizing an sound source distribution.
In a wave source image reconstruction by the hologram, a two dimensional interference observation is performed to obtain a two-dimensional interferogram (complex hologram), and the obtained interferogram is reconstructed, thereby displaying the wave source distribution. To be concrete, when an electromagnetic wave source is analyzed, a certain observation frequency is set, two antennas, that is, a fixed antenna and a mobile antenna are used for wave sensors, and a scanning observation plane is set at a position separate from an observation objective. While the mobile antenna is being moved in the scanning observation plane, a signal from the observation objective is received by the two antennas, and at this point of time when the mobile antenna is at each point in the scanning observation plane, a complex correlation value of signals from the two antennas is obtained, whereby the complex interferogram is obtained. The mobile antenna is called also a scanning antenna.
As an active observation, a reference wave is radiated from one antenna and the reference wave is received by the other antenna. Subsequently, the complex correlation value between the original reference wave and the received signal may be obtained.
A method by the radio wave hologram or the acoustic wave hologram can be applicable to a measurement of an electric field intensity distribution in a three-dimensional space as well as to an observation of a wave source distribution on a two-dimensional surface. For example, under conditions where a Fresnel's approximation is established, using Aoki's method (Aoki et al., "Numerical Second Dimension Fresnel's Conversion Method", Electronic, Communication and Information Society Vol. J57-B, No. 8, pp.511-518, August, 1974), the three-dimensional wave source distribution has been obtained in such manner that when a distance between the scanning observation plane and the wave source plane is z.sub.s, a size at the scanning observation plane be D.times.D and a wave source image reconstruction focal distance is z.sub.b, z.sub.b is varied under the condition of z.sub.s .ltoreq.D, thereby obtaining a plurality of reconstructed images, and the three-dimensional wave source distribution is obtained from the plurality of reconstructed images. This method involves many restrictions on actual use, such as operation of varying z.sub.b under the condition of z.sub.s .ltoreq.D.
Regarding analysis of a wave distribution and a wave source image by a radio wave hologram and an acoustic wave hologram, the inventor of the present invention has proposed a novel measurement method and apparatus for reconstructing a wave source image and a calculating method for reconstruction of a wave source image in, for example, Japanese Patent Laid-Open Application No. 201459/96 (JP, A, 08201459), Japanese Patent Laid-Open Application No. 134113/97 (JP, A, 09134113), Japanese Patent Laid-Open Application No. 133721/97 (JP, A, 09133721), Japanese Patent Application No. 265997/96 and Japanese Patent Application No. 268249/96. Especially, in above JP, A, 08201459 document, the present inventor proved that in the region where Fraunhofer's approximation can be applicable, presence of two reconstruction images observed at different frequencies makes it possible to estimate the three-dimensional wave source distribution without the restriction by the size D of the scanning observation plane and the necessity to vary the z.sub.b. In the method disclosed in JP, A, 08201459, in the position where a primary wave source is looked out, a wave source image is reconstructed by acquiring two dimensional interferogram by two frequencies. A propagation delay time from the scanning observation plane to each reconstructed wave source image is considered, thereby rearranging each wave source in a three-dimensional space. Waves from the rearranged wave sources are re-irradiated, thereby synthesizing them. Thus, a three-dimensional wave intensity is estimated. Hereinafter, descriptions for this method will be made. First, a hologram observation model will be described with reference to FIG. 1.
A hologram observation plane 301 is set on an xy-plane (i.e., z=0) including a origin O. It is assumed that a wave source disposed plane 302 exists in a position apart from the hologram observation plane 301 in a z-axis direction by z.sub.s. Assuming that a position vector of an observation point on the hologram observation plane 301 and a position vector of a current source on the wave source disposed plane 302 be R and R', respectively, an electric field E(R) produced at a observation point by the current source J(R') is expressed using dyadic Green function G for a three-dimensional space by the equation (1.1). ##EQU1##
Here, assuming that a vector effective length of a receiving antenna be l.sub.e, a distance r between the observation point and the current source satisfies an equality r&gt;&gt;.lambda. for a wavelength .lambda. (=c/f: c is a light velocity) corresponding to an observation frequency f, a receiving voltage V at the antenna is expressed by the equation (1.2), EQU V=gl.sub.e .multidot.E (1.2)
where g is constant.
Therefore, a receiving voltage at the observation point is expressed by the equations (1.3) and (1.4) as follows, ##EQU2## where V.sub.h and V.sub.v are antenna receiving voltages for a horizontally polarized wave and a vertically polarized wave, respectively, and l.sup.h.sub.e and l.sup.v.sub.e are vector effective lengths of a antenna for a horizontally polarized wave and a vertically polarized wave, respectively.
If the equation (1.5) is established, ##EQU3## the equation (1.3) will be expressed by the equation (1.6), ##EQU4##
FIG. 2 is a diagram for explaining a mirror image observation model applying the foregoing hologram observation model. It is assumed that in the point 402 in front of (i.e., in a positive direction of the z-axis of) the hologram observation plane 401 (z=0), a primary wave source current J.sub.0 (x.sub.0, y.sub.0, z.sub.0) exists. Moreover, it is assumed that a reflection plane 403 is arranged so as to be parallel with the z- and y-axes. It is assumed that an observation electric field at an observation point p on the hologram observation plane 401 is E.sub.p (x.sub.a, y.sub.a), a point 402 is symmetrical to a mirror image point 404 with respect the reflection plane 403 when viewed from the observation point p, and a mirror image wave source current assumed to be observed at the mirror image point 404 is J(x.sub.s, y.sub.s, z.sub.s). It is also assumed that a distance between the origin O and the point 402 is r.sub.o, a distance between the observation point p and the mirror image point 404 is r', and a distance between the origin O and the mirror image point 404 is r'.
By the approximation expressed by the equation (2.1) using a Fraunhofer's approximation, ##EQU5## the following equations (2.2) and (2.3) are established, ##EQU6## where u=k.sub.0 x.sub.s /z.sub.s, v=k.sub.0 y.sub.s /z.sub.s, k.sub.0 is the wave number in a free space, and .mu..sub.0 is a magnetic permeability in a vacuum. From the equations (2.1) and (2.3), a propagation delay time will be expressed by the equation (2.4). ##EQU7## Therefore, the hologram observation give the following equations (2.5) and (2.6). ##EQU8##
If the reconstructed image is obtained for two frequencies that are angle frequencies .omega..sub.1 and .omega..sub.2 (.omega..sub.1 .noteq..omega..sub.2), and the approximation expressed by the equation (2.7) is carried out, ##EQU9## the following equations (2.8), (2.9) and (2.10) are established, ##EQU10## and moreover, the following equations (2.11) and (2.12) are established. ##EQU11## Therefore, the receiving electric field at any point at the three-dimensional space will be expressed by the equations (2.13) and (2.14). ##EQU12##
Therefore, by reconstructing the wave source image by the two frequencies, the wave intensity at the three-dimensional space can be estimated, allowing to know a three-dimensional distribution of the wave.
However, in the case of the above-mentioned conventional method recited in JP, A, 08201459 document, an error may not be neglected which is caused by errors in the vector effective length of the receiving antenna and the three-dimensional dyadic Green function. This error becomes larger as the distance between the hologram observation plane and the wave source point becomes shorter. It also becomes larger as angle formed by the wave source point relative to the z-axis when viewed from the observation plane becomes larger. Specifically, since in the conventional method described above, a strict prove compensation is not conducted and Fraunhofer's approximation is employed, there has been a possibility to produce a large error of an estimated amplitude of the wave source close to the observation plane. FIG. 3A is a diagram showing a reconstructed amplitude of the wave source by the conventional method, and FIG. 3B is a diagram showing a reconstructed amplitude in the case where only the directivity of the antenna is compensated. In FIG. 3B, for the directivity of the antenna, a directivity is employed considering the vector effective length. In FIGS. 3A and 3B, a more accurate observation is performed as a level becomes closer to 1.0. As apparent from FIGS. 3A and 3B, according to the above described conventional method, the estimation of the wave source distribution in the three-dimensional space produces an observation error of about 10 dB and leaves an error of about 2 dB in spite of the compensation of the directivity of the antenna.
Further, in case of reconstructing a wave distribution by a radio wave hologram using a fixed antenna and a scanning antenna, the above conventional method is disadvantageous in that scanning of the antenna must be repeated for each observation frequency when visualizations at a plurality of frequency spectra are performed. This is caused by that an apparatus for acquiring an interferogram has a PLL (phase-locked loop) circuit in general and that a phase offset of the PLL circuit is generated when the observation frequency is switched. An absolute phase of a received signal must be measured at each observation frequency when a time response waveform is observed. However, according to the above conventional method, the absolute phase for the fixed antenna side cannot be estimated when the observation frequency is changed.
Next, the present state of the technology for the estimation of the stereoscopic direction of the antenna, which is an applicable field of the hologram observation, will be described.
In recent years, techniques to seize the directivity of the antenna in a working state in an actually set-up place have been required. For example, in a base station antenna used in a cellular mobile communication system, in order to prevent interference between cells at the same frequencies and to modify a cell size in a working state, a variable beam tilt antenna, which is capable of varying a beam tilt, has been used. When such kind of the antenna is used, the directivity of the antenna is sometimes changed after setting up the base station. Such changing of the directivity of the antenna involves a possibility that troubles such as unnecessary side lobes may occur, so that an estimation of the directivity in working state is required.
The evaluation of the directivity of the antenna has heretofore been performed using a radio wave darkroom. Although an evaluation of the directivity in a horizontal plane is easy to perform, an evaluation of a stereoscopic directivity wherein directivities in all directions of an antenna must be observed is difficult for the reason of restriction of the radio wave darkroom. In addition, since an evaluation of the directivity of the antenna in the working state in the actual setting-up circumstance is extremely difficult because of an error due to various kinds of reflection waves and actual impossibility of stereoscopically viewing the observed antenna from all directions. For example, a base station antenna in the mobile communication system is generally set up on a rooftop of a building in a city area. In such circumstances for the setting-up of the antenna, various kinds of reflection waves from adjacent buildings and roads are present so that both are simultaneously received. On the other hand, since an electric field measurement can be conducted only on the ground, it was impossible to seize a stereoscopic directivity of the base station antenna.
Next, the present state of the technology for displaying the result acquired by a hologram observation will be described.
In case of a radio wave observation, a vertical polarization component and a horizontal polarization component can be easily separated to each other. In a conventional method, an wave source image obtained by reconstructing a hologram image for an identical measurement objective is displayed in images in four representation manners by (1) an amplitude distribution of the horizontal polarization component, (2) a phase distribution of the horizontal polarization component, (3) an amplitude distribution of the vertical polarization component, and (4) a phase distribution of the vertical polarization component. However, expert knowledge regarding induction mode and phase difference is necessary for analyzing such image data.
For example, there are several methods for displaying a current distribution and a field distribution as follows: (1) a method for indicating an arrow sign whose length corresponds to the intensity, disclosed in G. Vecchi et al., Proc. 26th European Microwave Conference, Prague, pp. 560-564, September, 1996; (2) a method using a bird's-eye view in which height is set in accordance with the intensity, disclosed in X. Ding et al., Proc. 26th European Microwave Conference, Prague, pp. 574-578, September, 1996; (3) a method using contour lines, disclosed in Y. Gao et al., Proc. 26th European Microwave Conference, Prague, pp. 662-664, September, 1996, and in I. Okada, Technical Report of Electronic, Communication and Information Society, MW93-15, pp. 99-104 (1993-04); and (4) a method using color-coding, disclosed in F. Tilley, IEEE 1995 International EMC Symposium Record, pp. 435-439. These methods are disadvantageous in that amounts and kinds of information displayed in one graph or chart are small.